There are different aspects to this question. Firstly, conceptual skills are important, in other words, skills relating to the various strands of mathematics: algebraic, numerical, statistical, geometrical, probabilistic and spacial skills. These skills will be covered in the various topics but also in Fluency (below) which is about practising these types of skills until they are automatic.
Secondly, there are mathematical skills which are not linked to a particular strand of mathematics. These are skills like: problem solving, logic skills, use of technology, research skills and study skills.
All of these skills are important in different ways. Fluency is important for freeing up the working memory when solving problems. Having a good set of problem solving skills allows us to tackle an unseen problem and break it down into achievable parts. Research and study skills allow us to learn new things. Logic is a skills that employers are increasingly asking for in their employees. Finally, with the rapid devleopment in technology, it is vital that students can use technology to aid their understanding and solutions to problems.